2026 NCHS P1 Q23

The diagram below shows a panel made up of two identical parallelograms \(ABCD\) and \(PQCD\) overlapping each other in the region \(PBCD\). \(APBQ\) is a straight line and \(AP=PB=BQ\).

1. Show that triangle \(ADP\) and triangle \(BCQ\) are congruent. Give a reason for each statement you make.[3]
2. Given that angle \(BQC=75^\circ\), \(CD=10.5\text{ cm}\) and \(CQ=6\text{ cm}\), calculate the length of \(DQ\).[3]